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Complexity_ITS 2019-03-21 04.46 pair #429991074
details
property
value
status
complete
benchmark
NestedLoop.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n119.star.cs.uiowa.edu
space
PLDI09
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.62674 seconds
cpu usage
12.28
user time
11.8645
system time
0.415485
max virtual memory
1.88073E7
max residence set size
225636.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
12.15/5.16 WORST_CASE(Omega(n^2), O(n^2)) 12.15/5.17 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 12.15/5.17 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.15/5.17 12.15/5.17 12.15/5.17 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). 12.15/5.17 12.15/5.17 (0) CpxIntTrs 12.15/5.17 (1) Koat Proof [FINISHED, 1633 ms] 12.15/5.17 (2) BOUNDS(1, n^2) 12.15/5.17 (3) Loat Proof [FINISHED, 3441 ms] 12.15/5.17 (4) BOUNDS(n^2, INF) 12.15/5.17 12.15/5.17 12.15/5.17 ---------------------------------------- 12.15/5.17 12.15/5.17 (0) 12.15/5.17 Obligation: 12.15/5.17 Complexity Int TRS consisting of the following rules: 12.15/5.17 evalNestedLoopstart(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopentryin(A, B, C, D, E, F, G, H)) :|: TRUE 12.15/5.17 evalNestedLoopentryin(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb9in(A, B, C, 0, E, F, G, H)) :|: A >= 0 && B >= 0 && C >= 0 12.15/5.17 evalNestedLoopbb9in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopreturnin(A, B, C, D, E, F, G, H)) :|: D >= A 12.15/5.17 evalNestedLoopbb9in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb10in(A, B, C, D, E, F, G, H)) :|: A >= D + 1 12.15/5.17 evalNestedLoopbb10in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb6in(A, B, C, D, 0, D, G, H)) :|: 0 >= I + 1 12.15/5.17 evalNestedLoopbb10in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb6in(A, B, C, D, 0, D, G, H)) :|: I >= 1 12.15/5.17 evalNestedLoopbb10in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopreturnin(A, B, C, D, E, F, G, H)) :|: TRUE 12.15/5.17 evalNestedLoopbb6in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb8in(A, B, C, D, E, F, G, H)) :|: E >= B 12.15/5.17 evalNestedLoopbb6in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb7in(A, B, C, D, E, F, G, H)) :|: B >= E + 1 12.15/5.17 evalNestedLoopbb7in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb1in(A, B, C, D, E, F, G, H)) :|: 0 >= I + 1 12.15/5.17 evalNestedLoopbb7in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb1in(A, B, C, D, E, F, G, H)) :|: I >= 1 12.15/5.17 evalNestedLoopbb7in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb8in(A, B, C, D, E, F, G, H)) :|: TRUE 12.15/5.17 evalNestedLoopbb1in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb3in(A, B, C, D, E, F, E + 1, F)) :|: TRUE 12.15/5.17 evalNestedLoopbb3in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb6in(A, B, C, D, G, H, G, H)) :|: H >= C 12.15/5.17 evalNestedLoopbb3in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb4in(A, B, C, D, E, F, G, H)) :|: C >= H + 1 12.15/5.17 evalNestedLoopbb4in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb2in(A, B, C, D, E, F, G, H)) :|: 0 >= I + 1 12.15/5.17 evalNestedLoopbb4in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb2in(A, B, C, D, E, F, G, H)) :|: I >= 1 12.15/5.17 evalNestedLoopbb4in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb6in(A, B, C, D, G, H, G, H)) :|: TRUE 12.15/5.17 evalNestedLoopbb2in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb3in(A, B, C, D, E, F, G, H + 1)) :|: TRUE 12.15/5.17 evalNestedLoopbb8in(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopbb9in(A, B, C, F + 1, E, F, G, H)) :|: TRUE 12.15/5.17 evalNestedLoopreturnin(A, B, C, D, E, F, G, H) -> Com_1(evalNestedLoopstop(A, B, C, D, E, F, G, H)) :|: TRUE 12.15/5.17 12.15/5.17 The start-symbols are:[evalNestedLoopstart_8] 12.15/5.17 12.15/5.17 12.15/5.17 ---------------------------------------- 12.15/5.17 12.15/5.17 (1) Koat Proof (FINISHED) 12.15/5.17 YES(?, 15*ar_0 + 8*ar_2 + 22*ar_0*ar_1 + 22*ar_1 + 23) 12.15/5.17 12.15/5.17 12.15/5.17 12.15/5.17 Initial complexity problem: 12.15/5.17 12.15/5.17 1: T: 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopentryin(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopentryin(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb9in(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 0 /\ ar_1 >= 0 /\ ar_2 >= 0 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopreturnin(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= ar_0 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb10in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_3 + 1 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb10in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb6in(ar_0, ar_1, ar_2, ar_3, 0, ar_3, ar_6, ar_7)) [ 0 >= i + 1 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb10in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb6in(ar_0, ar_1, ar_2, ar_3, 0, ar_3, ar_6, ar_7)) [ i >= 1 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb10in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopreturnin(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_1 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= ar_4 + 1 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= i + 1 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ i >= 1 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4 + 1, ar_5)) 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb6in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) [ ar_7 >= ar_2 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 >= ar_7 + 1 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= i + 1 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ i >= 1 ] 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb6in(ar_0, ar_1, ar_2, ar_3, ar_6, ar_7, ar_6, ar_7)) 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7 + 1)) 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopbb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopbb9in(ar_0, ar_1, ar_2, ar_5 + 1, ar_4, ar_5, ar_6, ar_7)) 12.15/5.17 12.15/5.17 (Comp: ?, Cost: 1) evalNestedLoopreturnin(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 12.15/5.17 12.15/5.17 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalNestedLoopstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] 12.15/5.17 12.15/5.17 start location: koat_start
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